Geological and Atmospheric Sciences Publications Geological and Atmospheric Sciences

7-2007 Soft-bed experiments beneath Engabreen, Norway: regelation infiltration, basal slip and bed deformation Neal R. Iverson Iowa State University, [email protected]

Thomas S. Hooyer University of Wisconsin-Madison

Urs H. Fischer Antarctic Climate and Ecosystems Cooperative Research Centre

Denis Cohen Iowa State University, [email protected]

Peter L. Moore IFoowlalo Swta tthie Usn iaverndsit ay,dd pmooritione@ial wasorktate.se duat: http://lib.dr.iastate.edu/ge_at_pubs Part of the Geomorphology Commons, Glaciology Commons, and the Sedimentology See next page for additional authors Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ ge_at_pubs/144. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html.

This Article is brought to you for free and open access by the Geological and Atmospheric Sciences at Iowa State University Digital Repository. It has been accepted for inclusion in Geological and Atmospheric Sciences Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Authors Neal R. Iverson, Thomas S. Hooyer, Urs H. Fischer, Denis Cohen, Peter L. Moore, M. Jackson, G. Lappegard, and J. Kohler

This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/ge_at_pubs/144 Journal of Glaciology, Vol. 53, No. 182, 2007 323

Soft-bed experiments beneath Engabreen, Norway: regelation infiltration, basal slip and bed deformation

N.R. IVERSON,1 T.S. HOOYER,2 U.H. FISCHER,3 D. COHEN,1 P.L. MOORE,1 M. JACKSON,4 G. LAPPEGARD,5 J. KOHLER6 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa, 50011, USA E-mail: [email protected] 2Wisconsin Geological and Natural History Survey, 3817 Mineral Point Road, Madison, Wisconsin, 53705, USA 3Antarctic Climate and Ecosystems CRC and Australian Antarctic Division, Box 252-80, Hobart, Tasmania 7001, Australia 4Norwegian Water Resources and Energy Directorate (NVE), PO Box 5091, NO-0301 Oslo, Norway 5Department of Geography, University of Oslo, PO Box 1042, Blindern, NO-0316 Oslo, Norway 6Norwegian Polar Institute, Polar Environmental Center, NO-9005 Tromsø, Norway

ABSTRACT. To avoid some of the limitations of studying soft-bed processes through boreholes, a prism of simulated till (1.8 m 1.6 m 0.45 m) with extensive instrumentation was constructed in a trough blasted in the rock bed of Engabreen, a temperate glacier in Norway. Tunnels there provide access to the bed beneath 213 m of ice. Pore-water pressure was regulated in the prism by pumping water to it. During experiments lasting 7–12 days, the glacier regelated downward into the prism to depths of 50– 80 mm, accreting ice-infiltrated till at rates predicted by theory. During periods of sustained high pore- water pressure (70–100% of overburden), ice commonly slipped over the prism, due to a water layer at the prism surface. Deformation of the prism was activated when this layer thinned to a sub-millimeter thickness. Shear strain in the till was pervasive and decreased with depth. A model of slip by ploughing of ice-infiltrated till across the prism surface accounts for the slip that occurred when effective pressure was sufficiently low or high. Slip at low effective pressures resulted from water-layer thickening that increased non-linearly with decreasing effective pressure. If sufficiently widespread, such slip over soft glacier beds, which involves no viscous deformation resistance, may instigate abrupt increases in glacier velocity.

1. INTRODUCTION Our goal was to avoid these difficulties by building and studying a 1.3 m3 prism of simulated till beneath Enga- The subglacial setting in which temperate ice rests on a soft breen, Norway, (Iverson and others, 2003) where tunnels bed is most important for modulating fast glacier flow and through the subglacial rock provide access to the bed. Our mobilizing basal sediment (Clarke, 2005). Interactions results provide a field demonstration of regelation infiltra- among water, ice and sediment in this environment can tion of ice into a till bed (e.g. Iverson and Semmens, 1995; result in abrupt temporal and spatial variations in glacier Clarke, 2005; Christoffersen and others, 2006), help velocity. On large scales these variations may be mani- illustrate the relationship between basal water pressure fested as surging (e.g. Clarke and others, 1984), spatio- and the coupling between ice and till (e.g. Fischer and temporal switching of ice-stream flow (e.g. Kamb, 2001) Clarke, 2001) and provide new insights into controls on the and lurching behavior of parts of ice sheets that has been vertical distribution of bed deformation (e.g. Boulton and measured directly (Bindschadler and others, 2003) and others, 2001). Associated analysis indicates that regelation inferred from seismicity (Ekstro¨m and others, 2003, 2006). infiltration occurred at rates in agreement with theory, and Also, very high rates of basal sediment transport have been a new model of ploughing clarifies how changes in the postulated for glaciers that are soft-bedded and warm- thickness of a water layer at the bed surface control the based (Hooke and Elverhøi, 1996; Dowdeswell and basal flow mechanism. Siegert, 1999). Moreover, under these conditions some of the most poorly understood of glacial landforms, such as drumlins (e.g. Boulton, 1987) and megascale lineations 2. BACKGROUND (e.g. Ottesen and Dowdeswell, 2006), are thought to have developed. 2.1. Regelation infiltration The most detailed observations of soft-bed processes In a process that Clarke (2005) calls regelation infiltration, beneath glaciers have been made with instruments temperate ice may move downward into the pores of inserted through boreholes drilled to the bed, from either subglacial sediment by melting and refreezing. Evidence for ice tunnels (e.g. Boulton and Hindmarsh, 1987) or glacier this process comes from laboratory experiments (Iverson, surfaces (e.g. Blake and others, 1992; Kamb, 2001). These 1993; Iverson and Semmens, 1995). Its rate is controlled by observations, although illuminating, have been limited by the bed-normal pressure gradient across the sediment layer the restricted range of instruments that can be inserted that has been entrained, which depends on the effective through boreholes. Moreover, interpretations are compli- pressure at the bed and the thickness of the layer. cated by ambiguities regarding instrument position, bed Although the isotopic composition (Iverson and Souchez, geometry and bed disturbance by hot-water drilling. 1996) and structure (Truffer and others, 1999; Christoffersen 324 Iverson and others: Soft-bed experiments beneath Engabreen

velocity to seemingly insignificant changes in stress (Bindschadler and others, 2003) indicates that even a small decrease in flow resistance caused by slip over a soft bed could affect flow dynamics over wide areas. The question of where most basal motion occurs and how it depends on water pressure still lacks a definitive answer, in part due to ambiguity in interpreting existing borehole data. For example, Tulaczyk and others (2000a) argued that up- glacier rotation of tiltmeters in basal till reflected expansion of till as pore-water pressure rose, rather than elastic relaxation in shear and associated slip of ice across the bed surface. Also, the processes operating at the bed surface are unclear. Movement there is assumed to occur by a combination of ice sliding past bed clasts that protrude upward into the glacier and ploughing of such clasts across the bed surface (Brown and others, 1987; Alley, 1989; Iverson, 1999). These models, however, have considered basal ice to be clean. If ice generally intrudes into sediment Fig. 1. Site of the till prism, access points to the bed of Engabreen pores, so ice-infiltrated sediment slides over the bed surface, and the bed morphology. The ice tunnel melted to the site of the till the physical relevance of these models is dubious. prism was started from the tunnel access to the bed. The vertical shaft was the site of the sliding velocity measurement. Contour 2.3. Profile of bed deformation interval 1 m. Some data indicate that when the bed shears, rates of shear strain generally increase upward toward the bed surface (Boulton and Hindmarsh, 1987; Boulton and Dobbie, 1998; and others, 2006) of some basal ice facies are consistent Boulton and others, 2001), so the velocity profile is with sediment entrainment by regelation infiltration, it may concave-down. Early discussion attributed this strain pattern be prevented or inhibited beneath glaciers. In fine-grained to an ad hoc rheological rule for till in which the rate of sediments interfacial-curvature and pre-melting effects shear deformation was assumed to be directly proportional (O’Neill and Miller, 1985; Rempel and others, 2004) can to the shear stress and inversely proportional to the effective hold water sufficiently tightly in the pore space to inhibit pressure (Boulton and Hindmarsh, 1987). Since effective refreezing there. Alley and others (1997) estimated that pressure, and hence shearing resistance, increases more regelation should be impeded for sediment grains smaller rapidly with depth than shear stress – at least in the absence than fine to medium silt. In addition, regelation infiltration of upwardly flowing pore water – shear-strain rates, may be inhibited by sliding of ice across the bed, with according to this rule, should decrease downward (Alley, frictional heat impeding refreezing (Alley and others, 1997). 1989). However, diverse laboratory studies do not support Field measurements have not yet demonstrated that this rheological rule (Kamb, 1991; Iverson and others, regelation infiltration occurs. Studying this process subgla- 1998; Tulaczyk and others, 2000a). These studies, in cially is important because it may provide a general agreement with most geotechnical literature, indicate that mechanism of sediment entrainment for wet-based glaciers the most appropriate first-order model for till is that of a (e.g. Iverson, 2000; Christoffersen and others, 2006). More- Coulomb material in which shear-strain rate is independent over, if regelation infiltration is common then, as noted by of shear stress. Boulton and others (2001), ice-infiltrated sediment, rather This finding has prompted other explanations for the than clean ice, overlies the wet sediment of the bed. Slip at deformation profile. Iverson and others (1998) suggested such an interface has not been studied. that shear zones in Coulomb till will migrate due to increases in shear-zone strength caused by shear-induced 2.2. Basal slip of ice over a soft bed dilation and an associated reduction in pore pressure, Resistance to basal movement of soft-bedded portions of thereby distributing strain as observed. Others have glaciers is commonly assumed to be equal to the deform- suggested that repeated water-pressure variations at the ation resistance of the bed (e.g. Paterson, 1994; Tulaczyk bed surface and associated downward diffusion of pore and others, 2000b; Bindschadler and others, 2003), such pressure would cause vertical migration of the locus of that the bed deforms in shear at its yield strength. There is shear that could lead to the observed profile (Tulaczyk, considerable evidence from modern glaciers, however, that 1999; Tulaczyk and others, 2000a). A third hypothesis under some conditions ice slips across the surface of the invokes movement of particles in till resulting from very bed, without shearing it significantly at depth (Blake and brief, local departures from quasi-static stress equilibrium others, 1994; Iverson and others, 1995; Hooke and others, caused by the failure of stress-bearing grain networks 1997; Boulton and others, 2001; Kamb, 2001; Truffer and (Iverson and Iverson, 2001). The frictional strength of the Harrison, 2006). In particular, some borehole experiments bed increases more rapidly with depth than the applied indicate that when basal water pressure is rising and high the shear stress, so the small force imbalances that drive grain bed relaxes elastically in shear up-glacier as slip occurs at movement tend to be smaller at depth than near the bed the bed surface (Fischer and Clarke, 1997; Iverson and surface. Thus, relative movements between grains and others, 1999). Some field evidence indicates that such slip resultant shear-strain rates tend to decrease with depth in can be responsible for major glacier speed-up events (Truffer the bed. This explanation for the concave-down profile is and Harrison, 2006). Also, extreme sensitivity of ice-sheet similar to that of Alley (1989) but relies on experimental Iverson and others: Soft-bed experiments beneath Engabreen 325

Fig. 2. Till prism in a flow-parallel cross-section with instruments.

studies of grain-bridge failure and grain displacements up-glacier side (Fig. 2). Lateral walls of the bedrock trough calculated from Newton’s second law rather than on the were irregular and sloped more gently than the headwall. Boulton and Hindmarsh (1987) rheological rule. Three 32 mm boreholes were drilled through the rock bed from the down-glacier end of the trough to the underlying rock tunnel (Fig. 1), spanning a distance of 4 m. Two of 3. RESEARCH QUESTIONS these boreholes were for instrument cables. A pipe that We address three questions in our field experiments: (1) Can extended downward into the rock tunnel was cemented in a temperate glacier entrain till by regelation infiltration and, the third borehole to use as a conduit for pumping water if so, are rates of infiltration comparable to those predicted upward from the tunnel to the bed surface. by theory? (2) How does partitioning of basal movement No source of till was available in the tunnel system, so a between slip at the bed surface and bed deformation depend synthetic till was used. Supraglacial till was available in the on basal water pressure and what processes at the bed end moraines of Engabreen, but these moraines lie 700 m surface are responsible for this partitioning? (3) Can the below and 5 km away from the site of the experiment, concave-down velocity profiles measured by Boulton and making transport of a sufficient volume of this till to the bed- colleagues be reproduced and, if so, does this strain pattern access point prohibitively laborious and time-consuming. necessarily require a specific till rheology (Boulton and We thus manufactured several cubic meters of synthetic till Hindmarsh, 1987), dilatant strengthening (Iverson and by digging sediment from the floor of the rock-tunnel others, 1998) or basal water-pressure fluctuations (Tulaczyk system. This sediment was the product of blasting, which and others, 2000a)? produces a power-law relationship between the number and sizes of grains similar to that of some basal tills (Hooke and Iverson, 1995). The synthetic till was, by mass, 10% gravel, 4. METHODOLOGY 70% sand and 20% silt and clay, and the relationship Engabreen is a temperate outlet glacier of the Svartisen ice between the number and sizes of grains was indeed well cap in northern Norway. Its bed consists of gneiss and schist fitted by a power law (Fig. 3). The relatively small silt-and- bedrock with meter- to decameter-scale undulations and no clay fraction, characteristic of many basal tills (e.g. overlying till layer, except in rare circumstances (e.g. Hooke Haldorsen, 1981; Hooke and Iverson, 1995; Truffer and and Iverson, 1995). Tunnels in the rock beneath the glacier others, 1999), caused the till’s permeability to be high and have been excavated as part of a hydropower installation. thereby reduced the likelihood that its dilation or contrac- One of these tunnels extends to the ice–bed interface tion during shear would produce non-hydrostatic pore (Fig. 1), where the glacier is 213 m thick and slopes at 108. pressures (e.g. Moore and Iverson, 2002). Avoiding this A removable door across the mouth of the tunnel prevents complication helped clarify interpretations. ice from squeezing into it. This tunnel is sufficiently dry Approximately 3 tons of simulated till were added to the during fall, winter and early spring to provide safe access for trough in layers, 50–100 mm thick, and various instruments subglacial experiments. The Svartisen Subglacial Laboratory were added to the till as the trough was filled (Fig. 2). To is housed beneath the glacier in a larger tunnel nearby and measure shear deformation, vertical columns of four has provided infrastructure for studies of various basal tiltmeters were placed in the till prism spanning its thickness processes (Jansson and others, 1996; Cohen and others, at two locations, and vertical columns of beads, 16 or 2000, 2005, 2006; Iverson and others, 2003; Lappegard and 18 mm in diameter, were positioned within 0.1 m of the others, 2006). An essential part of this infrastructure is a tiltmeter columns for excavation after the experiment. The warm-water drill that allows tunnels (usually 5m2 in cross- tiltmeters consisted of biaxial, electrolytic cells (Fredericks section) to be melted through ice along the bed. Company, model 0717-2201) mounted in plastic cylinders, 16 mm in diameter and 50 mm long. Three pore-pressure 4.1. Till prism and instruments sensors were installed in the till prism, up-glacier from the To study soft-bed processes, a till prism was constructed in a mouth of the water-entry pipe. Two of these were placed bedrock trough beneath the glacier. A tunnel was melted 1.3 m up-glacier from the pipe at different heights above the through the basal ice to a relatively flat section of the bed, bed; the third was placed 0.5–0.6 m up-glacier from the pipe 10 m from the mouth of the bed-access tunnel (Fig. 1). (Fig. 2). A disk-shaped earth-pressure (EP) cell, oriented A trough was blasted in the bed there that was 1.8 m long, horizontally in the till, recorded total normal stress exerted 1.6 m wide and 0.45 m deep. The trough was oriented over a circular sensing face 102 mm in diameter. A strain- roughly parallel to bedrock striae and was deepest on its meter, 0.33 m long, was placed vertically in the till. This 326 Iverson and others: Soft-bed experiments beneath Engabreen

pumped for a few hours to the glacier sole. In 2001 a high- discharge pump, operated in the rock tunnel, was used to pump a steady discharge of 8 L s–1. In 2002 a lower- discharge (0.13 L s–1) pump was used. During these pump tests, water pressure varied from nearly atmospheric to above the ice-overburden pressure. Following the 2001 experiment, a tunnel was melted through the ice back to the till prism. Although every effort was made to expose the prism without eroding it with water from the drill, some disturbance of the prism was unavoid- able. Nevertheless, bead-displacement profiles were meas- ured, undisturbed portions of the till prism were closely examined, some instruments were recovered and undis- turbed samples were collected to compute the final till Fig. 3. Particle-size distribution of the simulated till used in the porosity. Unfortunately, logistical problems prevented ex- experiments. Mass fractions were obtained by mechanical sieving, and the number and mean diameter of each particle-size class were cavation of the prism after the 2002 experiment. determined using the method described by Hooke and Iverson Ancillary laboratory data were collected to character- (1995). The exponent of the power-law fit is –3.37. The coefficient ize some of the mechanical properties of the simulated of determination (r 2) of the fit is 0.99. till. A series of drained direct-shear experiments (Lambe and Whitman, 1969) were performed on remolded specimens at various normal stresses (10–500 kPa) to determine the friction angle and cohesion of the till. In piston-like instrument, which had anchors at its ends that addition, the till was compressed incrementally in a gripped the till, recorded till expansion or contraction along fixed-ring consolidometer (Lambe and Whitman, 1969) to a direction parallel to its long axis. Both the earth-pressure provide baseline data on till compressibility, hydraulic cell and the strainmeter were free to rotate in the till during diffusivity and permeability. The till specimen was then shear, although it was hoped, based on laboratory obser- unloaded and reloaded to provide data for the case of vations of clast rotation in shearing till (Hooyer and Iverson, overconsolidated till. 2000), that the disk-shaped pressure cell would not rotate out of the plane of shear. The pore-pressure sensors, earth- pressure cells and strainmeters were vibrating-wire sensors 5. RESULTS (Geokon models 4500S-500, 4800X-1-500 and 4430-X, Figures 4 and 5 show records from tiltmeters, earth-pressure respectively). When the prism was completed, gravel-sized cells, strainmeters and the mean record from pore-pressure clasts, painted gold, were embedded partway in the till to sensors during the 2001 and 2002 experiments. As in most mark the bed surface. borehole studies of soft-bed processes, some instruments did Cables from the instruments were fed down two of the not return meaningful signals throughout the experiments. In boreholes to the underlying tunnel. All instruments had 2001 all of the tiltmeters in one of the two columns (not separate cables, reducing the chance of mechanical inter- shown in Fig. 4) stopped working 2 days into the experiment. action of instruments. Hollow rubber stoppers, which had During both years, other tiltmeters near the ice–till interface been threaded onto each bundle of cables, were ham- failed late in the experiments. Also, a multiplexer malfunc- mered into the mouths of the boreholes to inhibit water tion in 2002 resulted in the loss of 5 days of tiltmeter data leakage from the bed. All instruments in the prism were (Fig. 5a and b). excited and logged with a Campbell CR10x data logger The experiments began with closure of the ice tunnel, and multiplexer. causing progressively increasing contact of ice with the Also, 11 m directly down-glacier from the till prism, prism (Figs 4 and 5). During closure, tiltmeters recorded sliding velocity was measured at the mouth of a vertical shaft irregular deformation that began hours before the down- used in other experiments (Fig. 1) (Cohen and others, 2000, ward stress on the prism, recorded by the earth-pressure 2005). This was done by measuring the displacement of an cell, began to increase. In 2001 this stress ramped up to a anchor entrained in the ice. The anchor was connected to a value commensurate with the ice thickness (2000 kPa) in thin cable that extended into the rock tunnel below, where 1.6 days and then became steady (Fig. 4b). In 2002 the an extensometer (Unimeasure, model HX-PA-60) recorded stress on the earth-pressure cell increased similarly but the withdrawal of the cable during sliding. after 1 day abruptly peaked at 1500 kPa and then fell to 900 kPa before becoming steady (Fig. 5c). In both years 4.2. Procedure extension of the strainmeter began to occur prior to the In March 2001 and April 2002, experiments were increase in stress on the earth-pressure cell. This extension conducted that lasted 7–12 days. In each experiment, after reached a peak during closure, then declined slightly the till prism was constructed, the ice tunnel was before becoming steady at approximately the time when evacuated, and the door across the mouth of the bed- the stress on the earth-pressure cell became steady access tunnel was closed. After a period of several days, the (Figs 4b and 5c). ice tunnel shrunk until tiltmeters, the earth-pressure cell and For 2–3 days after closure was over, stress on the earth- the strainmeter indicated that ice had begun closing on the pressure cells remained steady (Figs 4 and 5). Pore pressure surface of the prism. Once reasonably steady conditions in remained very near atmospheric during this period in 2001 the till prism had been achieved, a series of pump tests and crept up slightly, to 300 kPa, in 2002. In 2001, were conducted. In each of these tests, water at 28Cwas tiltmeters recorded little deformation during this period Iverson and others: Soft-bed experiments beneath Engabreen 327

Fig. 4. Time series from the 2001 experiment. Signals from the four tiltmeters of column 2 are labeled according to the original heights of their upper ends above the base of the till prism. All sensors of column 1 stopped working 2 days into the experiment and are not shown. Pump tests correspond to the two periods of elevated pore- water pressure.

(Fig. 4a). In 2002 a preliminary pump test was conducted on Fig. 5. Time series from the 2002 experiment. Signals from the 18 April (Fig. 5c) that was quickly aborted when tiltmeters tiltmeters, which were placed originally in vertical columns, are delivered physically untenable signals that led to the labeled according to the original heights of their upper ends above diagnosis of the multiplexer problem. Once this problem the base of the till prism. Beginnings of pump tests correspond to was corrected, the tiltmeters indicated that some deform- abrupt increases in pore-water pressure. ation of the prism had occurred during the previous 5 days (Fig. 5a and b), perhaps during the later stages of closure or the preliminary pump test. 1800 kPa with the pump on continuously. After the pump –1 Sliding velocity was relatively steady at 44 7ma in was shut off, water pressure decayed at a rate two orders of 2001. In 2002, no velocity measurement succeeded. magnitude slower than in 2001. Thus the drainage path However, sliding velocity measured in 2003 (Cohen and away from the till prism was far less conductive in 2002 others, 2005) fell within the same narrow range as in 2001, than in 2001. so the velocity was probably similar in 2002. During pump tests each year, pore pressure at the up- glacier and down-glacier locations of pore-pressure sensors 5.1. Pump-test hydrology (Fig. 2) varied nearly synchronously and equivalently, but During the last stage of these experiments, repeated pump the direction and magnitude of the hydraulic gradient within tests were conducted, which differed in 2001 and 2002. In the prism differed (Fig. 6). In 2001 prior to the pump tests, 2001 a discharge of 8 L s–1 was pumped to the prism until a the pore-pressure gradient (measured parallel to the length hydraulic connection along the ice–rock interface adjacent of the prism over a longitudinal distance of 0.8 m) was near to the prism was established with the mouth of the access zero. The pump tests caused water flow up-glacier across tunnel (Fig. 1). This connection was indicated by turbid the prism, as indicated by a negative pore-pressure gradient water flowing into the access tunnel. Pumping was then (<–200 kPa m–1). The value of this gradient gradually stopped, both to minimize erosion of the till prism by water became less negative during the pump tests (Fig. 6a). During and because pore pressure could not be sustained. Pressure 2002 before the pump tests, there was a small negative pore- decreased to near atmospheric within minutes of turning pressure gradient, indicating minor water flow up-glacier off the pump. Two pump tests of several hours were across the prism. During and after pump tests, however, the completed in 2001 (Fig. 4b), with a maximum pore-water gradient reversed (became positive) (Fig. 6b). This indicates pressure of 1600 kPa. that water introduced to the down-glacier edge of the prism In 2002 during pump tests at the smaller discharge (Fig. 2) drained largely down-glacier away from the prism, (0.13 L s–1), hydraulic connection with the mouth of the rather than, as in 2001, up-glacier across the prism. Also, in access tunnel was never established. Rather, during the 2002 the pore-pressure gradient across the prism was a four 3–5 hour pump tests starting 19 April (Fig. 5c), water maximum of 15 kPa m–1, less than 10% of the negative flowed from the till prism along an unknown drainage gradient during pumping in 2001. path. During the first of these pump tests, pore pressure Another aspect of the pump-test hydrology is that the total cycled about the ice-overburden pressure because the stress recorded by the earth-pressure cells was perturbed by pump had to be switched on and off every 5–20 min to pumping water to the glacier sole. Increases in pore pressure avoid sustained pore pressure in excess of the ice- resulted in increases in total stress on the earth-pressure cells overburden pressure. In the subsequent three pump tests, that were sometimes >50% of the pore-pressure increase pore pressure was sustained at a relatively steady value of (Figs 4b and 5c). 328 Iverson and others: Soft-bed experiments beneath Engabreen

Fig. 6. Up-glacier and down-glacier pore-water pressure and pore- Fig. 7. (a) Strain records calculated from rotation of tiltmeters pressure gradient during and after pump tests of (a) 2001 and (column 2) in 2001. Distances are heights of the tops of tiltmeters (b) 2002. A positive gradient implies down-glacier water flow across above the base of the prism. The highest tiltmeter in the column the till prism. Duration of pump tests shown with dotted lines. stopped working at 1930 h, 26 March. Pore-water pressure is the mean value from the three sensors. (b) The last 8 hours of the tiltmeter record shown in (a), spanning the end of the second pump 5.2. Tiltmeter records test, together with mean effective pressure on the bed and the signal from the strainmeter. Mean effective pressure is the difference During the early stages of pump tests, tiltmeters accelerated between the total normal stress on the bed measured with the earth- their rotation down-glacier but then generally either stopped pressure cell and the mean pore-water pressure. The strainmeter rotating or began rotating up-glacier until some time after was not normal to the bed at this stage of the experiment but was the pump test was over. If, as in past studies (e.g. Blake and sufficiently upright that abrupt contraction at the end of the pump others, 1992), tiltmeters are assumed to rotate passively test reflects contraction of the prism. during shear, till shear strain, , can be computed from the ¼ = down-glacier tilt angle, d,as 1 2 tan d. In Figure 7a shear strain is plotted for the four tiltmeters of the column that functioned during the period spanned by the pump tests. column 2 (placed with its upper surface 0.42 m above the To allow direct comparison of shear-strain records during base of the rock trough and 0.04 m below the bed surface) this period, shear-strain values were set to zero early on behaved differently during the third pump test (Fig. 8, 25 March. Shear-strain rates, as indicated by the slope of the bottom panel); shortly after this test began, this tiltmeter plots, increased initially during pump tests but eventually increased its rate of rotation to a relatively steady value more became negative (up-glacier rotation), as high pore-water than an order of magnitude larger than that exhibited by any pressure was sustained. This reversal in shear direction other tiltmeter during either year. This tiltmeter stopped occurred in both pump tests but was pronounced in the working about 4 hours later. second, longer test. At the end of the pump tests, when pore Tiltmeter rotation and associated strain and time-averaged pressure fell rapidly, there was renewed down-glacier shear, strain rates generally increased upward toward the bed sur- although this shear occurred after, rather than during, the face (Figs 4a, 5b and 7a). Tiltmeter rotation was interpolated pore-pressure decrease and associated increase in effective linearly over depth intervals in the bed centered on the tilt- pressure (Fig. 7b). Overall, shear-strain variations during meters to estimate vertical profiles of horizontal till displace- pump tests were affected by, but did not mirror, changes in ment (Fig. 9). The compaction of the till prism due to the effective pressure on the bed. pressure of the ice, described in section 5.3, was accounted Tiltmeters from pump tests of the 2002 experiment for in generating these profiles. Profiles were generally con- behaved similarly. Figure 8 shows shear strains, set to zero cave-down over both the period spanned by the pump tests prior to the pump tests, indicated by the two uppermost and the longer period between the start of the experiment and tiltmeters of each column that delivered reliable signals. when one tiltmeter in the columns failed (Fig. 9). The primary There was a clear tendency for tiltmeters to rotate up-glacier exception was column 1 in 2002, in which shear strains were or stop rotating down-glacier either at the beginning of or greater at depth, due to irregular deformation early in the during pump tests. However, the highest tiltmeter in experiment during ice closure on the till (Fig. 5a). Iverson and others: Soft-bed experiments beneath Engabreen 329

Fig. 8. Strain records calculated from rotation of tiltmeters in 2002. Uppermost two tiltmeters in each column that worked for most of the pump tests are shown (the two uppermost tiltmeters in column 1 are not shown because they had both stopped working by the end of the first pump test). Distances are heights of the tops of the tiltmeters above the base of the prism. Note the high shear strains indicated by the tiltmeter record in the lowest panel. The top of this tiltmeter (uppermost tiltmeter of column 2) is inferred to have been Fig. 9. Deformation profiles computed from tiltmeter rotation deflected by sliding ice at 1700 h, 20 April. during (a) 2001 and (b) 2002. Profiles labeled ‘Pump tests’ were computed based on tiltmeter rotation during only the periods spanning the pump tests. Profiles labeled ‘Long-term’ were computed over the full period when all tiltmeters functioned 5.3. Post-experimental observations properly (20–26 March in 2001; 11–21 April in 2002). Thus, the Excavation of the till prism in 2001 revealed that its initial long-term profiles include the effects of irregular deformation upper surface was not the bed surface at the end of the during ice closure on the till. experiment. Painted clasts placed at the initial bed surface had basal ice above them identical to dirty basal ice usually observed at the bed of Engabreen (2–11% debris by volume (Cohen and others, (2005)). However, below the painted when the till prism could not be excavated, to construct the clasts there was a layer of ice-cemented till (Fig. 10). In the velocity profiles of Figure 9b. undisturbed part of the prism that could be excavated, this Bead columns placed near each of the two tiltmeter ice-cemented layer was 50–80 mm thick. The contact columns in 2001 were successfully exposed and measured between the basal ice and ice-cemented till was sharp, (Fig. 11). Several beads at the top of both columns were and there was flow-parallel asymmetry of this contact found displaced down-glacier but at a high angle to the around some clasts (Fig. 10), consistent with ice sliding past glacier flow direction. We inferred that these beads were them. The contact between the ice-cemented till and the scraped by ice from the bed surface during ice-tunnel underlying till (the final bed surface) was also sharp, with closure, so data from these beads are not plotted in clear separation between the two materials. Figure 11. Down-glacier bead displacements near tiltmeter Samples collected for bulk density measurements in 2001 column 1, which stopped working during the first 2 days of indicated a final mean bulk density for the till prism of the experiment, indicate major shear strain focused near the 2190 30 kg m–3, corresponding to a porosity of 19.6 bed. Bead displacements near tiltmeter column 2 indicate a 1.2%. Samples collected before the experiment had a weakly concave-down velocity profile, similar in shape to mean dry bulk density of 1830 50 kg m–3, or a porosity that constructed from the signals of the tiltmeters from this of 33.4 1.8%. The measured reduction in porosity corres- column (Fig. 11). However, the bead profile indicates shear ponded to mean thinning of the till layer of about 18% in displacements a factor of three larger than those indicated 2001. This amount of thinning was assumed also in 2002, by the tiltmeter signals. This difference apparently reflects till 330 Iverson and others: Soft-bed experiments beneath Engabreen

Fig. 11. Bead profiles from 2001. Tiltmeter column 1 stopped working about 2 days into the experiment, so a profile calcu- lated from only tiltmeter column 2 (see also Fig. 9a, ‘Long- term’) is shown.

by ice from above it (Figs 4a and 5a and b). This Fig. 10. Basal ice after excavating part of the till prism from the interpretation is supported by deformation that began before experiment of 2001. The painted clast was initially halfway buried stress on the earth-pressure cells had begun increasing in the surface of the till prism when ice closed on it. After the (Figs 4b and 5c). Bulldozing is also indicated by one of the experiment, ice-cemented till extended 50–80 mm below the clast. bead profiles from 2001, which indicated a steep velocity Overlying the clast was basal ice with sparse debris like that usually gradient near the base of the prism (Fig. 11). Deformation of observed at the bed of Engabreen (Cohen and others, 2005). Sliding the till prism during ice closure is also illustrated by the direction was from left to right. strainmeters, which extended substantially, either due to shear that stretched the instruments or vertical extension associated with bulldozing (Figs 4b and 5c). The subsequent deformation during the 3 days of the experiment after the contraction of these instruments that occurred as stresses on uppermost tiltmeter in column 2 stopped working; the the earth-pressure cells were increasing is interpreted as displacement record computed from column 2 (Fig. 11) does reflecting consolidation of the till as ice closed on it from not include that period. above, although this underestimates the true consolidation, due to rotation of the strainmeters from their initially vertical 5.4. Ancillary laboratory data orientation during deformation. Given the irregular deform- Results of direct-shear tests, conducted until steady shear ation during closure, our discussion focuses primarily on stresses were attained, yielded a friction angle of 32.38 with bed deformation during the pump tests. zero cohesion, consistent with the high sand content of the till (Fig. 12a). Till compressibility, , (Freeze and Cherry, 6.2. Total normal stresses 1979; Clarke, 1987) decreased with increasing normal Although conditions in the prism became relatively steady stress, as is expected due to the resultant reduction in once closure was complete, in 2002 the steady-state porosity, and was about an order of magnitude smaller pressure on the earth-pressure cell was about 50% (900– during reloading of the till once it had been overconsoli- 1000 kPa) of that expected from the ice thickness (Fig. 5c). dated (Fig. 12b). Hydraulic diffusivity, D, (Freeze and Cherry, This is interpreted as reflecting rotation of the instrument, so 1979) was estimated using the rate of change of consoli- that its sensing face deviated substantially from horizontal; ¼ dation after loading increments (e.g. Bowles, 1992); D when granular materials are loaded vertically in confined –5 2 –1 1.0–3.2 10 m s (Fig. 12b). Owing to the negligibly compression, horizontal stresses can be less than half the small compressibility of water, hydraulic conductivity, K,is applied stress (Lambe and Whitman, 1969, p. 127). Thus, ¼ well approximated by K wgD , where w is water this instrument probably did not record the total downward density and g is gravitational acceleration. Values of stress on the prism. In 2001 there was little rotation of the –7 K calculated from D and decreased from 5 10 to earth-pressure cell, as indicated by its near-horizontal –9 –1 5 10 ms with increasing normal stress. orientation upon excavation of the prism and by its steady- state signal, which was commensurate with the ice-over- 6. ANALYSIS AND DISCUSSION burden pressure (Fig. 4b). The increase in total stress on the earth-pressure cells 6.1. Closure during pump tests when pore-water pressure was in- The irregular deformation recorded by the tiltmeters during creased (Figs 4b and 5c) was probably a product of the closure is interpreted to reflect partial bulldozing of the till limited footprint of the pressure pulse. The dilation of till prism by ice closing on its sides, prior to loading of the prism and upward movement of ice that would result from a Iverson and others: Soft-bed experiments beneath Engabreen 331 spatially uniform increase in basal pressure was impeded by ice outside the margins of the till prism that was outside the pressure-pulse footprint. Thus, no upward movement of ice was permitted, other than elastic flexure, so some of the increase in water pressure resulted in an increase in downward total stress on the prism. This result is a reminder that spatial gradients in basal water pressure can locally affect the total stress that ice exerts on the bed (e.g. Murray and Clarke, 1995; Lappegard and others, 2006). In 2001 this effect of water pressure on total normal stress was successfully measured and factored into calculations presented hereinafter; this was not possible for the experiment of 2002, in which the earth-pressure cell rotated. 6.3. Regelation infiltration Observations after the 2001 experiment indicate that the position of the bed surface (interface between dirty ice and ice-free till) moved into the prism 50–80 mm over the part of it that could be successfully excavated, with resultant entrainment of till (Fig. 10). Although the till prism could not be excavated in 2002, the abrupt, sustained increase in rotation rate of the uppermost tiltmeter of column 2 (Fig. 8, bottom panel) provides evidence that downward migration Fig. 12. (a) Results of direct-shear tests with the simulated till. As of the bed surface also occurred during that year’s 8 indicated by the regression, the friction angle is 32.3 with a experiment. On the afternoon of 20 April ( 1700 h), the standard error of 28. The cohesion is 1 kPa with a standard error of rate of rotation of this tiltmeter increased abruptly by more 10 kPa. (b) Compressibility and hydraulic diffusivity of the till as a than an order of magnitude. This higher rotation rate was function of total normal stress, determined from tests with a fixed- commensurate with a change in horizontal velocity across ring consolidometer. Diffusivity remained relatively constant with the tiltmeter equal to 60% of the sliding speed. We infer that increasing normal stress because reductions in permeability were the upper end of the tiltmeter was deflected by sliding ice, compensated by reductions in compressibility. thereby dramatically increasing its rotation rate. The failure of this tiltmeter 4 hours later is consistent with this explana- tion. The top of this tiltmeter was originally 40 15 mm granular layer at a speed, vr, given by below the bed surface. Accounting for the tiltmeter’s KsðÞPi Pw rotation, which would have reduced the elevation of its vr ¼ , ð1Þ upper end, the top of this tiltmeter would have been H 55 15 mm below the initial bed surface when its top was where Ks is a constant fully derivable from first principles deflected by ice. Unfortunately, the uppermost tiltmeter (Philip, 1980), H is the thickness of the ice-infiltrated from the other column (Fig. 5a) never delivered a meaningful sediment layer, Pi is the normal stress acting on the upper signal, so yielded no information about the position of the boundary of that layer and Pw is the pore-water pressure in bed surface with time. the bed. Ks is proportional to the apparent conductivity of Possible mechanisms for downward migration of the bed sediment to ice, such that Ks g, with the ice density, is surface include freeze-on by regelation in the lee of a bed analogous to the conductivity of Darcian flow. The rate of obstacle, net freeze-on of water by conductive cooling, net change in the thickness of the ice-infiltrated layer, dH/dt,is freeze-on by supercooling and regelation infiltration (Alley dH ¼ v m_ , ð2Þ and others, 1997). Refreezing in the lee of a bed obstacle dt r can be ruled out because, although the trough that where m_ is the basal melt rate. Neglecting heat advected by contained the till prism was blasted on the down-glacier basal water and dissipated by water flow, the basal melt rate side of a subdued bump, this bump had a wavelength of depends on the flux of heat from the bed, q , and on the several meters, far larger than expected for significant b heat flux produced by basal motion at a velocity U and regelation (e.g. Paterson, 1994). Also, net freeze-on by under a shear stress : conductive cooling can be precluded because Engabreen is a fully temperate glacier with basal ice containing more than _ ¼ 1 ðÞþ ð Þ m qb U , 3 2% water (Cohen, 2000). The bed sloped down-glacier at nL the site of prism, both locally and regionally, so freeze-on by where n is the porosity of the ice-infiltrated till layer and L is supercooling is not a viable hypothesis. the volumetric latent heat of fusion. Combining Equations (1) We conclude that the most likely mechanism for the and (2) and integrating yields   downward migration of the bed surface was regelation ðÞ _ 2 þ _ ¼ Ks Pi Pw m t mH : ð Þ infiltration. To test this hypothesis, theory grounded on the H _ 1 exp ð Þ 4 regelation model of Philip (1980) can be used to calculate m Ks Pi Pw the depth of infiltration as a function of time for comparison Equation (4), together with Equation (3), was used to with our observations. Following Iverson and Semmens calculate the thickness of the ice-infiltrated till layer as a (1995) and Iverson (2000), temperate ice will regelate into a function of time (Fig. 13) for comparison with both the direct 332 Iverson and others: Soft-bed experiments beneath Engabreen

Table 1. Parameter values used to calculate infiltration depth

Parameter (units) Value Source

2 –1 –1 –15 Ks (m Pa s ) 2.1–2.6 10 Iverson and Semmens (1995, fig. 2) L (Jm–3) 3.06 108 Paterson (1994) m_ (m a–1) 0.54–1.06 Equation (3) n 0.2–0.34 Measured Average Pi Pw (kPa) 1840 Measured in 2001 1620 Measured in 2002 –2 qb (W m ) 1.65 Calculated from air temperature in rock tunnel U (m a–1) 44 Measured (kPa) 100–500 Cohen and others (2005)

evident had the time-averaged value of Pi – Pw during the experiments been smaller. Our results also indicate that the Fig. 13. Regelation infiltration depth during the experiments of component of ice motion parallel to the bed surface did not 2001 and 2002, calculated using regelation theory grounded on the grossly impede regelation. Our pump tests, however, model of Philip (1980) and adapted by Iverson (2000). Ranges of probably did impede regelation by increasing pore-water parameter values used in the calculation to arrive at upper and pressure in the prism and causing transient separation lower bounds are listed in Table 1. Error bars for the 2001 data point between ice-infiltrated till and the prism, as discussed in reflect the range of intrusion depths observed upon excavating the section 6.4. The latter of these effects could not be till prism. Error bars for the 2002 data point reflect the uncertainty of the position of the top of the tiltmeter that is inferred to have been incorporated in the calculation of infiltration depth deflected by the glacier sole (see text and Fig. 8, bottom panel). (Fig. 13) but, owing to the limited duration of the pump tests, did not have a perceptible effect on the results.

6.4. Water-layer thickness and glacier–bed coupling observation at the end of the 2001 experiment (Fig. 10) and Periods of up-glacier tiltmeter rotation during pump tests the thickness inferred in 2002 from the abrupt increase in (Figs 7 and 8) are interpreted as periods of relaxation of the tiltmeter rotation rate (Fig. 8, bottom panel). Table 1 lists the prism in shear when slip occurred at the bed surface. During ranges of parameter values used to calculate the upper and these events, the shear traction supported by the bed surface lower bounds of the model prediction. Basal melt rates were became less than the bulk yield strength of the till, halting higher than normal (0.54–1.06 m a–1). They were calculated permanent deformation of the till down-glacier and causing using the measured value of U, ranges of local measured by its elastic relaxation up-glacier (Iverson and others, 2003). Cohen and others (2005) at Engabreen, ranges of n defined An alternative interpretation is that up-glacier rotation by the initial and final porosity of the prism, and ranges of qb simply reflected periods of till dilation associated with indicated by the temperature gradient in the rock bed. This increasing pore-water pressure, which would cause a gradient was controlled by the air temperature of the rock tiltmeter tilting down-glacier to rotate up-glacier (Tulaczyk tunnel 4 m below the till prism (28C); one-dimensional heat and others, 2000a). This hypothesis is not tenable in this case flow was assumed to calculate qb, using a thermal conduct- because substantial up-glacier rotation occurred commonly ivity appropriate for granitic rock (3.3 W m–1 8C–1). Values of when water pressure was either steady or decreasing (Figs 7a Ks in Table 1 reflect the melting-point depression for air- and 8). Moreover, there were sometimes lags between pore- saturated ice and the range of till porosity considered pressure changes and tiltmeter response (Fig. 7b). (Iverson and Semmens, 1995). In the experiments, Pi – Pw A past interpretation of similar tiltmeter records attributed varied with time, so the time-averaged value was used slip of ice over the bed to thickening of a water layer (Table 1). This value provides a good estimate of the total between clean ice and the bed surface (Iverson, 1999). This infiltration depth over the duration of the experiments but thickening was thought to submerge some particles at the smooths irregularities in the rate of infiltration-depth increase bed surface, thereby concentrating shear stresses on larger caused by unsteady Pi Pw. particles sufficiently to activate ploughing and associated Although the thickness of the ice-infiltrated layer was slip of the glacier across the bed. In the case of the ice- observed only once during each year, Figure 13 indicates infiltrated till layer overlying the bed surface in these that the model, with no adjustment of parameters, is in experiments, this water layer can be considered to be a thin good agreement with these observations. This agreement zone of very high porosity (Fig. 14), probably caused by a supports the hypothesis that regelation infiltration entrained combination of elastic uplift of the glacier sole and till at the top of the prism, despite the higher-than-normal winnowing of particles at the bed surface by water flow basal melt rate. Moreover, the good agreement indicates through this porous zone. interfacial-curvature and pre-melting effects that can hold Unlike past studies, in this case the water-layer thickness water tightly in the till pores did not impede regelation can be independently estimated as a function of time and discernibly, although these effects might have become compared with the record of till deformation. Although the Iverson and others: Soft-bed experiments beneath Engabreen 333

Fig. 14. Ice-infiltrated till sliding over a water-saturated till bed. A water layer separates much of the ice-infiltrated till from the bed. Only particles of sufficient size protrude through the layer and plough during slip of the glacier across the bed surface. water layer could not be observed directly, near-synchronous variations in water pressure at the up-glacier and down- glacier positions in the prism suggest that flow across the prism occurred primarily at the bed surface rather than through the till pores (Fig. 6). Time lags between the two pressure signals were discernible but <5 min in duration. Had water flowed up- or down-glacier primarily through the till, the minimum diffusive time lag would have been on the 2= Fig. 15. (a) Water-layer thickness during pump tests of 2001, order of xd D, where xd is the lateral distance between sensors (0.8–0.9 m) and D is the maximum hydraulic calculated from the constant water discharge during pumping and diffusivity of the till (3 10–5 m2 s–1). For these experiments, the measured pressure gradient. Shear-strain record is from the 2= uppermost tiltmeter in column 2 (see Fig. 7a). Dashed line shows xd D was greater than 5.5 hours, far longer than the lags when the uppermost tiltmeter began sustained up-glacier rotation, observed. However, if sensors were a few centimeters away indicating slip at the bed surface, and points to the associated from the water layer at the glacier sole, as a result of water-layer thickness. (b) Water-layer thickness after pump tests of regelation infiltration of the bed, with essentially instant- 2002, calculated using the water discharge squeezed from the aneous transmission of pressure through the water layer, then consolidating till prism. Upper and lower bounds of water-layer the timescale for vertical diffusion through the till to the thickness are shown, corresponding to virgin and reloaded till, water layer would have been on the order of a few minutes, respectively. Shear-strain record is from the uppermost tiltmeter in as observed, rather than hours. Most water, therefore, must column 1 that worked during all of the pump tests. Dashed lines have flowed across the prism through a water layer at the indicate when sustained up-glacier rotation of this tiltmeter began after pump tests. bed surface, and the pressure gradient recorded by the sensors was comparable to that driving flow through this layer (Fig. 6). Thus, if, in addition to the pressure gradient, the water directions from the mouth of the borehole across the prism, discharge through the layer is known, the water-layer the spatially averaged discharge per unit width across the thickness, dw, can be estimated, for the case of laminar prism and between the two pressure sensors was ¼ –3 2 –1 flow (e.g. Weertman, 1972; Engelhardt and Kamb, 1997): Qm 1.2 10 m s . This value yields a Reynolds number less than 1000 (670), so the laminar-flow assump- 1 3 12Qm w tion of Equation (5) is correct (Vennard and Street, 1982). dw ¼ , ð5Þ Pg Using this value of Qm and the pressure gradient of Figure 6a in Equation (5) to calculate dw during the two where Qm is the mean water discharge per unit width across pump tests of 2001 yields noisy values of 0.4–1.0 mm 8 the prism, w is the dynamic viscosity of water near 0 C, (Fig. 15a). This estimate assumes that ¼ 1:0 is a good Pg is the pressure gradient between the water-pressure approximation due to the limited area of real contact sensors, ignoring the negligible difference in sensor eleva- between particles in ice and the bed – an assumption tion, and is the fraction of the layer’s cross-sectional area justified in section 6.5. Up-glacier rotation of tiltmeters, that is not blocked by particles that span the layer. This interpreted to reflect slip of ice across the bed surface, equation applies strictly to steady-state flow. However, the occurred at dw 0.7 mm in the second pump test when the characteristic period required for steady flow to develop transition from bed deformation at depth to sustained slip 2 = after a change in Pg is dw , where is the kinematic occurred most clearly (Fig. 15a). In 2002 the same viscosity of water (e.g. Batchelor, 1967). This period is on the calculation is not possible because during pumping the order of 1 s for a 1 mm thick layer, so Equation (5) is pressure gradient was positive (Fig. 6b), indicating that water appropriate for Pg fluctuating over the much longer periods introduced to the down-glacier end of the prism did not flow of interest herein. up-glacier across the prism but rather escaped down-glacier. In 2001 Pg was negative (Fig. 6a), indicating that water Thus, the discharge across the prism during pump tests from pumped to the down-glacier end of the prism flowed up- that year is unknown. However, the water-layer thickness glacier across the prism. Assuming uniform radial flow in all can be estimated in 2002 during the periods following pump 334 Iverson and others: Soft-bed experiments beneath Engabreen

Table 2. Constants used to calculate water-layer thickness, sub- falling (2002) water pressure. Alternatively, it may reflect an mergence ratio and the slip parameter overestimate of the water discharge across the prism in 2001, when considerable discharge was observed entering Constant Value Source the mouth of the horizontal access tunnel, down-glacier (units) from the prism (Fig. 1). If more water escaped down-glacier from the water entry point than flowed up-glacier across the m 3.37 Measured (Fig. 3) prism, then the 2001 water-layer thickness would have been NF 21.8 Equation (11); Senneset and Janbu (1985) overestimated by an amount proportional to the flow n 0.3 Measured asymmetry. This and other uncertainties, such as the poorly RL (mm) 0.001 Measured known true azimuth of water flow at the bed surface, RU (mm) 8.0 Measured 3 highlight that these are crude estimates of water-layer Vt (m ) 0.98 Measured w (m) 1.62 Measured thickness. (8) 15 Senneset and Janbu (1985) Despite these uncertainties, however, these data indicate (8) 32.3 Measured (Fig. 12a) that water-layer thickness is a major factor modulating the w (Pa s) 0.0018 Vennard and Street (1982) tendency for glacier slip over the bed surface. This has been 1.0 Assumed assumed but not demonstrated in previous studies (Brown and others, 1987; Alley, 1989; Iverson, 1999). 6.5. Model of basal slip by ploughing tests. After pumping was stopped, water pressure decreased These results indicate that when basal water pressure and slowly in the prism, as did the down-glacier gradient in discharge are sufficiently large at a till bed, ice slips across water pressure (Fig. 6b). The dominant source of water the bed rather than deforming it at depth. This observation is flowing in the water layer during these periods would have consistent with those from several other glaciers (Blake and been pore-water that was squeezed from the till prism as others, 1994; Engelhardt and Kamb, 1998; Iverson and effective pressure on the prism increased. If all water others, 1999; Truffer and Harrison, 2006). Also, our results produced by this till consolidation flowed down-glacier confirm the expectation that when water pressure is through the water layer toward the side of the prism where sufficiently low, the bed does not deform at depth owing water had escaped during pumping, then the mean dis- to its high shear strength (e.g. Fig. 4). charge per unit width across the prism between the pressure Our goal now is to develop a slip model that reproduces sensors was this behavior, incorporating the effect of the water-layer V dP thickness. The model must describe friction between the Q ¼ t w , ð6Þ m w dt glacier sole and the bed, bearing in mind that regelation infiltration caused ice-infiltrated till, rather than mildly dirty where is the till compressibility (Fig. 12b), Vt is the volume ice, to be in contact with the till surface. Friction at this of the till prism upstream of the down-glacier pressure contact will depend on resistance to ploughing of particles sensor and w is the width of the prism (Table 2). Equation (6) that are sufficiently large to span the water layer, so these ignores the compressibility of water, which is small relative particles are both held in the ice-infiltrated till of the glacier to that of till (Freeze and Cherry, 1979), and the flux of water sole and protrude into the bed, as shown in Figure 14. In from basal melt, which was a negligibly small fraction of the contrast to the case of clean ice resting on a soft bed, in discharge of water squeezed from the till during consoli- which sliding of ice by the classical mechanisms (e.g. dation. Note that till compressibility probably decreased Lliboutry, 1979) may limit the shear traction on some with time after pumping, as effective stress increased and particles rather than ploughing (e.g. Brown and others, the porosity of the till decreased during consolidation, as 1987; Iverson, 1999), intergranular friction within the ice- indicated by the consolidometer tests (Fig. 12b). Substituting infiltrated till of the glacier sole will inhibit the classical Equation (6) into (5) yields the water-layer thickness during sliding mechanisms. Thus, we consider the shear traction on till consolidation after the pump tests of 2002: the soft bed to result exclusively from resistance to 1 3 ploughing of individual particles through the bed surface, ¼ 12 Vt w dPw : ð Þ dw 7 so that resistance to ploughing of particles through the wet P w dt g bed is always less than resistance to movement of particles Numerical values of dw were obtained during the periods through the ice-infiltrated till. Particles effectively act as after pump tests by fitting a power function to Pw with asperities at the base of the ice-infiltrated till layer that drag time and differentiating it, using the regressions of as a across the bed, which yields locally around them. The function of effective pressure (Fig. 12b), and applying smallest of these particle asperities are drowned in the water measured values of Pg (Fig. 6b). Upper and lower bounds layer and do not contribute to the shear traction on the bed of water-layer thickness are shown in Figure 15b, using surface (Fig. 14). compressibility values measured for virgin and reloaded till, The bed-parallel component of force exerted on respectively. ploughing particles, Fx, depends on the ploughing resist- For the three pump tests in 2002 for which this ance of the bed, s (bed-parallel stress exerted by the bed ¼ calculation was possible, down-glacier deformation of till on particles in the ice). Thus, Fx s(A – As), where A is was reactivated at water-layer thicknesses of 0.05– the total area of the bed and As is area of the bed 0.25 mm (Fig. 15b), somewhat thinner than when slip was submerged in the water layer. The quantity, A – As, is the initiated in 2001 (0.7 mm). This difference may reflect area of the bed in direct contact with particles protruding system hysteresis, such that the water-layer thickness from the glacier sole. The bed-normal weight of the necessary for slip was different during rising (2001) and glacier, Fz, is partitioned between ploughing particles and Iverson and others: Soft-bed experiments beneath Engabreen 335

water under a pressure Pw (e.g. Clarke, 2005). Thus, Substituting Equations (9) and (10) into Equation (8) and ¼ þ ¼ = Fz p(A – As) PwAs, where static stress equilibrium defining the normalized effective pressure as Pe Pe P0 requires that p is the resistance to penetration of particles yields the friction coefficient at the bed surface in terms of downward into the soft bed. The ratio between Fx and Fz, only dimensionless variables: after dividing both expressions by the total area of the : ¼ 0 5ÀÁNFPe : ð Þ bed, yields a friction coefficient, , for the glacier–bed I 12 I N P þ 1 P S interface: F e e R ðÞ An analogous friction coefficient, T, characterizes the ¼ s 1 fs ð Þ I ðÞþ , 8 overall resistance of the till bed to shear. Again neglecting p 1 fs Pwfs till cohesion, the shear strength of till, s , is given by the ¼ where fs is the fractional area of the bed submerged in the Coulomb–Terzaghi criterion: s Pe tan . Dividing both water layer. Thus, the shear traction on the bed due to sides of this equation by the total normal stress, P0, yields the ploughing is IP0, where P0 is the total normal stress on friction coefficient for till shear: the bed. ¼ P tan : ð13Þ A geotechnical theory of the movement of cones and T e piles through sediment (Senneset and Janbu, 1985), applied For values of Pe that satisfy I < T, the glacier will slip previously to subglacial ploughing (Iverson, 1999, 2004; across the bed by ploughing, rather than shearing it at depth. Fischer and others, 2001) and tested in experiments Thus, dividing Equation (13) by Equation (12) yields a slip (Senneset and Janbu, 1985; Iverson and others, 1994), parameter, s , which predicts whether slip will occur as a provides clear guidance for estimating the penetration function of P : e  resistance, p, and ploughing resistance, s: ÀÁ ¼ þ SR : ð Þ s 2 Pe 1 Pe tan 14 p ¼ NFPe ð9Þ NF ¼ : ð Þ s 0 5NFPe, 10 For s > 1, there will be slip by ploughing; for s 1, the glacier sole will grip the bed sufficiently to deform it at a where P is the effective pressure (P – P ). N is a e 0 w F shear stress equal to the bed shear strength. dimensionless bearing-capacity factor that depends on the The constants NF and in Equation (14) are well known, friction angle, , of the sediment and the orientation of but computing s from Pe also requires estimating SR, the conjugate slip surfaces in till near the ploughing element, described by the angle (Iverson and others, 1994): submergence ratio. SR depends on Pe through its effect on the  water-layer thickness and also depends on the size distri- ¼ 2 þ ðÞ2 tan : ð Þ bution of ploughing particle asperities on the glacier sole. To NF tan e 11 4 2 establish SR as a function of Pe , we first assume that the size Use of Equations (9) and (10) acknowledges that till is a distribution of ploughing particle asperities reflects the till Coulomb material, in which resistance to deformation is grain-size distribution. The number of grains, N, of radius R is ¼ –m independent of deformation rate and linearly dependent on given by the relation N kR , where k and m are fitted constants (Fig. 3). As shown in Appendix B, the submergence Pe. Laboratory experiments with till support this idealization ratio, as a function of water-layer thickness, dw, is then (Kamb, 1991; Iverson and others, 1998; Tulazcyk and others,  2000a), with the exception of the study of Ho and others d 3m R3m 1 S ¼ w L , ð15Þ (1996) in which steady-state deformation rates were not R R3m d 3m 1 n achieved. Cohesion is assumed to be zero, which was true, U w within error limits, for the till of the sediment prism where RL and RU are the upper and lower size limits of the grain-size distribution. The empirical relationships between (Fig. 12a); even in clay-rich tills with non-zero cohesion, cohesion is usually subordinate to the frictional component dw and Pe during the pump tests of 2001 (Fig. 15a) and during of till strength except at very low effective pressures. The the till consolidation that followed the pump tests of 2002 (Fig. 15b) are shown in Figure 16. During these periods there coefficient 0.5 in Equation (10) is the ratio of the transverse to plan-view cross-sectional areas of ploughing clasts in were exponential decreases in dw with increasing Pe . Using contact with till. This value of the ratio is appropriate for these relationships to specify dw in Equation (15), submer- spherical clasts buried halfway in the bed – a reasonable gence ratios from 6 to 38 are indicated over the measured mean position for ploughing particles (Brown and others, ranges of Pe , such that 86–98% of the bed area was 1987; Iverson, 1999), although values of this coefficient for submerged (Fig. 16). This result supports our assumptions individual particles probably vary through nearly the full that was close to 1.0 in Equations (5) and (7) (Table 2) and possible range (0–1.0). Moreover, Equation (10) applies only that ploughing particles were isolated sufficiently to have if excess pore pressures did not develop in the zone of non-interacting deformation fields. More importantly, these compression in till down-glacier from ploughing particles calculations indicate the general form of the function SR(Pe ); (e.g. Iverson, 1999). Scaling arguments, tested in laboratory submergence ratios, like dw, decreased exponentially with ploughing experiments (Thomason 2006), indicate that the increasing Pe . high hydraulic diffusivity of the till used in the prism Various functions that describe an exponential reduction –5 2 –1 (10 m s ) prevented excess pore pressures (Appendix A). in submergence ratio, SR, with increasing Pe (Fig. 17a) were Finally, Equations (9) and (10) are strictly valid only for considered in Equation (14) to explore how the slip deformation fields near ploughing particles that do not parameter s varies with Pe . For values of SR comparable interact, an assumption justified hereinafter. to those indicated by the data at low effective pressures (trial To rewrite Equation (8) in a more convenient form, we cases i–iii in Fig. 17a), slip over the bed ( s > 1) is predicted define the ratio of the submerged to unsubmerged fractions for sufficiently small and sufficiently large values of Pe , ¼ of the bed as the submergence ratio, SR fs /(1–fs). with bed deformation only at intermediate values. These 336 Iverson and others: Soft-bed experiments beneath Engabreen

6.6. Distribution of bed deformation The observation from tiltmeter rotations that shear-strain rates generally increased upward toward the bed surface (Figs 7 and 9) agrees with observations of Boulton and col- leagues within natural subglacial till layers (Bouton and Hindmarsh, 1987; Boulton and Dobbie, 1998; Boulton and others, 2001). The bead data are less illuminating because they include the irregular deformation (e.g. bull- dozing) that accompanied closure of ice on the prism. The bead data also include the period of melting when the till prism was exposed. Removal of the weight of ice from the top of the prism’s down-glacier end by melting could have resulted in slump-related deformation. This may explain why so much of the till deformation recorded by the beads occurred during the last 3 days of the experiment, after the failure of the uppermost tiltmeter in column 1 (Fig. 11). Unfortunately, no tiltmeter data were successfully logged during the exposure of the prism by melting, so this hypothesis cannot be checked. The concave-down velocity profiles that developed in these experiments allow us to conclude that several processes are not necessary for distributed deformation of till. Any explanation that requires viscous deformation resistance can be precluded, since experimental data on a number of tills provide no evidence for it (Clarke, 2005), and there is no reason to assert that this till should have anomalous mechanical properties. Dilatant strengthening (Iverson and others, 1998), which can lead to pseudo- viscous effects (Moore and Iverson, 2002), can be precluded owing to the high diffusivity of the till (Appendix C). Multiple water-pressure fluctuations at the bed surface, with diffusion of pore pressure to various depths in the till (Tulaczyk and others, 2000a), can also be dismissed; water Fig. 16. Calculated water-layer thicknesses and submergence ratios pressure varied nearly simultaneously and uniformly in the during the two pump tests of 2001 and during the periods of till consolidation following the three final pump tests of 2002. The prism (Fig. 6) due to its high diffusivity. Moreover, during a 2002 values are minima because the compressibility of the till upon single pump test, most of the thickness of the prism sheared reloading was used to compute water-layer thickness; owing to till (Fig. 7a). shear between pump tests and associated dilation, the till We favor the hypothesis that strain that increases in compressibility may have been higher, approaching the value for magnitude toward the bed surface results simply from virgin till (see Fig. 15). decreasing friction with decreasing depth in the bed (Iverson and Iverson, 2001). This friction is briefly and locally overcome when grain bridges fail at various depths in the predictions are in broad agreement with our tiltmeter bed. Movement in the bed depends on the magnitude of the observations (e.g. Figs 7 and 8) and observations elsewhere resultant stress imbalances, which will tend to be largest (e.g. Blake and others, 1994; Iverson and others, 1999). near the bed surface where frictional resistance is smallest. Only for values of SR smaller than those indicated by our With stress imbalances largest near the bed surface, relative data (case iv in Fig. 17a) is slip not predicted at low effective displacements among grains are largest there also, resulting pressures. For linear reductions in SR with increasing Pe , in shear strain that increases upward. values of the slip parameter indicate that the observed switching from bed deformation to slip of ice by ploughing under effective pressures approaching zero is far less likely 6.7. Effects of prism size (Fig. 17b). Thus, the tendency for the water-layer thickness An important consideration is whether the small size of the and the submerged area of the bed to change most rapidly at prism affected these results, particularly the tendency for ice low effective pressures appears to help instigate switching to slip across the bed surface during periods of sufficiently between basal flow mechanisms. sustained high pore pressure. Although the down-glacier The result that slip by ploughing prevails at sufficiently end of the trough that contained the till was tapered (Fig. 2), high effective pressures (Fig. 17a and b) stems from the longitudinal stress gradients in the prism may have impeded factor of 0.5 in the expression for ploughing resistance its shear deformation. Nevertheless, the prism did deform in (Equation (10)). This factor (the ratio of transverse to plan- shear between pump tests when pore pressure was lower view cross-sectional areas of ploughing particles in contact (Fig. 8). Thus, the conclusion that the bed surface was with till) results from only partial penetration of particles preferentially weakened by pumping relative to the till at in the bed and causes ploughing resistance that is less depth is sound. than resistance to bed shear as Pe approaches 1.0 in The small footprint of the prism also prevented the Equation (14). expected feedback between basal water pressure and the Iverson and others: Soft-bed experiments beneath Engabreen 337 rate of basal ice movement; any change in the resistance to basal motion over the area of the prism would not have caused a significant change in basal ice velocity, owing to lateral and longitudinal stress gradients in the ice. However, the lack of this velocity feedback would not have affected the partitioning between slip and shear deformation of the bed. As noted, the intrinsic strength of till, as a Coulomb material, is independent of its deformation rate. Thus, neither the shear strength of the bed nor the drag on particle asperities ploughing through the bed surface would have been affected by changes in the rate of basal motion. Also, possible rate- strengthening associated with dilation and associated pore- pressure reduction (e.g. Moore and Iverson, 2002) was prevented by the high hydraulic diffusivity of the till (Appendix C). During pump tests shear stresses must have shifted Fig. 17. Slip parameter as a function of normalized effective between the till prism and adjacent bedrock as water pressure for various submergence ratios that (a) decrease pressure and discharge fluctuated. Similar stress reorgan- exponentially with increasing effective pressure, as was observed ization has been observed beneath soft-bedded glaciers in the experiments, and (b) decrease linearly with increasing previously (e.g. Fischer and Clarke, 1997; Iverson and effective pressure. Slip parameters indicate that the observed others, 1999; Kavanaugh and Clarke, 2001, 2006; Truffer switching between slip and bed deformation is more likely for the and others, 2001). Thus, we view the stress redistribution of exponential case. these tests not as an experimental artifact but as a small- scale example of stress redistribution prompted by spatially non-uniform changes in basal hydrology. the ice–till interface played no role in distributing this deformation. These observations demonstrate that small changes in 7. CONCLUSIONS water-layer thickness can prompt slip of glaciers over soft Our measurements provide the first field demonstration that beds. Such slip may result in abrupt increases in glacier glacier ice can infiltrate a soft bed with a till-like grain-size velocity, consistent with recent interpretations of obser- distribution and at rates consistent with regelation theory. vations at Black Rapids Glacier, Alaska, USA (Truffer and Unlike other proposed mechanisms of sediment entrain- Harrison, 2006). This mechanism of glacier motion over a ment, regelation does not require an adverse bed slope (e.g. soft bed needs to be considered in evaluating abrupt velocity Alley and others, 2003) or departures from fully temperate increases elsewhere (e.g. on the ice plain of Whillans Ice conditions (e.g. Christoffersen and Tulaczyk, 2003). As a Stream, West Antarctica (Bindschadler and others, 2003)). result, ice-infiltrated till, rather than relatively clean ice, may Resistance to basal movement may be overestimated by commonly be in contact with the surfaces of soft beds, equating it with the bed shearing resistance, as commonly contrary to existing treatments of slip at the bed surface done in models of soft-bedded glaciers (Alley, 1989; Clark (Brown and others, 1987; Alley, 1989; Iverson, 1999; and others, 1996; Licciardi and others, 1998; Tulaczyk and Kavanaugh and Clarke, 2006). others, 2000b; Fowler and others, 2001; Bindschadler and Consistent with expectation, the glacier slipped across others, 2003). In addition, estimates of basal sediment the bed surface at near zero pore-water pressure; deform- transport by bed deformation that neglect such slip (e.g. ation of the prism was activated by pumping water to it, Jenson and others, 1995; Dowdeswell and Siegert, 1999; which increased pore pressure and weakened the till. Siegert and Dowdeswell, 2002) may grossly overestimate However, deformation commonly ceased if pore-water sediment fluxes. pressure within a few hundred kilopascals of the ice- Regelation infiltration and slip by ploughing at low overburden pressure was sustained. During these periods, effective pressures cannot occur simultaneously, owing to ice slipped across the bed surface. This switching between the ice–bed separation required for slip. Periods of regelation bed deformation and slip at low effective pressure and slip are expected to alternate as basal water discharge occurred at sub-millimeter water-layer thicknesses, which and effective pressure change seasonally and diurnally. controlled the area of the bed subject to ploughing by The observation that regelation infiltration can leave ice- particle asperities at the base of the ice-infiltrated till. infiltrated sediment in contact with a soft bed indicates that Model calculations account for the observed slip at low slip resistance at the bed surface can be dominantly and high effective pressures and for bed deformation at frictional rather than viscous, contrary to most model intermediate effective pressures. Non-linear water-layer assumptions (e.g. Alley, 1989; Kavanaugh and Clarke, thickening with decreasing effective pressure reduced 2006). Thus, increases in the rate of basal motion will not friction at the bed surface more than in the till bed, be accompanied by increases in slip resistance. Unlike the causing slip at low effective pressures rather than bed case of clean ice on a soft bed, the rate strengthening deformation. provided by ice sliding past clasts partway lodged in the When the prism deformed, it sheared pervasively over glacier sole (e.g. Brown and others, 1987) will be inhibited most of its thickness. Shear strain generally decreased with or prevented in ice-infiltrated till. Moreover, the till bed, if it depth, yielding the concave-down velocity profile observed deforms at depth, will not rate-strengthen, except transiently in some previous studies. Viscous deformation resistance, under the specific range of parameter space that promotes dilatant strengthening and pore-pressure diffusion from dilatant strengthening (Moore and Iverson, 2002). 338 Iverson and others: Soft-bed experiments beneath Engabreen

With only frictional sources of slip resistance, the ice–bed Clark, P.U., J.M. Licciardi, D.R. MacAyeal and J.W. Jenson. 1996. interface can be mechanically more akin to a crustal fault Numerical reconstruction of a soft-bedded Laurentide ice sheet than what has traditionally been assumed (e.g. Paterson, during the last glacial maximum. Geology, 24(8), 679–682. 1994). We view the abrupt lurching behavior of parts of ice Clarke, G.K.C. 1987. Subglacial till: a physical framework for its sheets, like that observed in West Antarctica (Bindschadler properties and processes. J. Geophys. Res., 92(B9), 9023–9036. Clarke, G.K.C. 2005. Subglacial processes. Annu. Rev. Earth Planet. and others, 2003) and inferred beneath the Greenland ice Sci., 33, 247–276. sheet from far-field seismicity data (Ekstro¨m and others, Clarke, G.K.C., S.G. Collins and D.E. Thompson. 1984. Flow, 2003, 2006), as possible indications that glacier beds can be thermal structure, and subglacial conditions of a surge-type dominated over large areas by resistance to basal movement glacier. Can. J. Earth Sci., 21(2), 232–240. that is frictional rather than viscous (see also Tulaczyk, 2006). Cohen, D. 2000. Rheology of ice at the bed of Engabreen, Norway. Future research should explore whether this friction can J. Glaciol., 46(155), 611–621. decrease with increasing slip rate – an essential requirement Cohen, D., R.LeB. Hooke, N.R. Iverson and J. Kohler. 2000. Sliding for stick–slip motion on crustal faults (e.g. Scholz, 2002). of ice past an obstacle at Engabreen, Norway. J. Glaciol., 46(155), 599–610. Cohen, D., N. Iverson, T. Hooyer, U. Fischer, M. Jackson and P. Moore. 2005. Debris-bed friction of hard-bedded glaciers. ACKNOWLEDGEMENTS J. Geophys. Res., 110(F25, F02007). (10.1029/2004JF000228.) We thank M. Rousselot and A. Flint for help in the field, and Cohen, D., T.S. 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Local friction laws for glaciers: a critical review significant excess pore pressures do not develop if the and new openings. J. Glaciol., 23(89), 67–95. timescale for compaction of till down-glacier from plough- Moore, P.L. and N.R. Iverson. 2002. Slow episodic shear of granular ing particles is larger than the timescale for pore-pressure materials regulated by dilatant strengthening. Geology, 30(9), diffusion out of the compacted zone. The timescale for 843–846. compaction, tc ,is /Up, where is the characteristic length 340 Iverson and others: Soft-bed experiments beneath Engabreen

scale for compaction and Up is the velocity of the ploughing in the layer: particle. The value of is approximately equal to the k ÀÁ diameter of the ploughing particle (Thomason, 2006). The ¼ 3m 3m : ð Þ As dw RL B3 2 ðÞ3 m ðÞ1 n timescale for pore-pressure diffusion, td is /D, where is commensurate with the length of the diffusion path and D is Particles with radii larger than dw will tend not to be the hydraulic diffusivity. Owing to the dependence of td on submerged in the water layer. Integrating Equation (B2) 2, excess pore pressures will be most probable near the from dw to the radius of the largest particle in the till largest ploughing particles. If we choose the largest particles bed, R , with n ¼ 0, yields the area of the bed covered : U of our field experiments, then 0 02 m. We assume the by particles sufficiently large to span the water layer and velocity of ploughing particles to be equal to the measured hence plough: slip velocity of the basal ice, 44 m a–1, a reasonable ÀÁ assumption for particles in the ice-infiltrated till of the k 3m 3m Au ¼ R d : ðB4Þ glacier sole. The measured hydraulic diffusivity was 3 m U w –5 2 –1 ¼ 10 m s . Using these values, tc 14 300 s and Substituting Equations (B3) and (B4) into Equation (B1) ¼ td 40 s. Thus, owing to the high diffusivity of the simulated yields the submergence ratio as given by Equation (15). till, pore-pressure diffusion would have occurred far too rapidly to result in excess pore pressures sufficient to invalidate Equations (9) and (10). APPENDIX C A scaling argument similar to that of Appendix A and APPENDIX B supported by stress-controlled ring-shear experiments with various tills (Moore and Iverson, 2002) indicates that dilatant The area of the bed submerged by the water layer can be strengthening did not occur during shear of the till. Dilatant estimated from the water-layer thickness and the till strengthening can be precluded if the timescale for pore grain-size distribution. The submergence ratio, SR,isby dilation during shear is long relative to the timescale for definition pore-pressure diffusion into the dilating pores of the shear ¼ As ð Þ zone. For a shear zone of thickness h, the timescale for pore SR , B1 ’ Au dilation, tp,ish/vs , where vs is the shearing velocity and ’ is the dilatancy, the ratio of shear-zone dilation (thicken- where Au is the unsubmerged area of the bed in direct ing) to shear displacement. The timescale for pore-pressure contact with particle asperities on the glacier sole. To 2 determine A , note that the number of particles, N,of diffusion into the shear zone, tds,ish /D. In laboratory s ’ radius R is given by N ¼ kR–m, as indicated by Figure 3, experiments with two different basal tills varied, depend- where k and m are fitted constants. Assuming that, on ing upon porosity, between 0.01 and 0.25 (Moore and ’ ¼ average, particles are halfway embedded in the glacier Iverson, 2002). Choosing 0.25 to minimize tp, con- sidering the full till thickness (h 0.5 m) to maximize tds, sole, the area of particles, AR, occupied by clasts of size R and their associated porosity, n,isNR2/(1 – n). Thus, choosing the measured sliding speed for the shearing ¼ –1 velocity (vs 44 m a ) and using the measured hydraulic kR2 m –5 2 –1 ¼ 6 A ¼ : ðB2Þ diffusivity (D 10 m s ) yields tp 1.4 10 s and R ¼ 4 1 n tds 2.5 10 s. Thus, owing to the high diffusivity of the Integrating this equation from the radius of the smallest till, pore-pressure diffusion would have outpaced pore particle in the till bed, RL, to the water-layer thickness, opening by more than a factor of 50. Dilatant strengthening dw, yields an estimate of the area of particles submerged was therefore unlikely.

MS received 26 October 2006 and accepted in revised form 16 April 2007